If x+2y=2 and (x+y)2=9, what is the value of y?

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Discussion Overview

The discussion revolves around solving the equations x + 2y = 2 and (x + y)² = 9 to find the value of y. Participants explore the implications of the equations and the potential solutions.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the solution, stating that the answer is not -1 and suggests it should be 5.
  • Another participant provides a step-by-step approach to solving the equations, deriving x = 2 - 2y and then substituting into (x + y)² to find the solutions, noting the presence of two possible values for y.
  • The second participant emphasizes the importance of recognizing that every number has two square roots, which may have been overlooked.
  • A third participant acknowledges the clarification provided by the second participant, indicating a moment of realization about the problem.
  • A fourth post introduces an unrelated comment about another participant, which does not contribute to the mathematical discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the value of y, as there are multiple proposed solutions, and the initial confusion regarding the answer remains unresolved.

Contextual Notes

The discussion highlights the importance of considering all possible solutions when dealing with square roots, as well as the potential for oversight in mathematical reasoning.

Who May Find This Useful

Individuals interested in algebraic problem-solving, particularly those exploring quadratic equations and the implications of multiple solutions.

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If x+2y=2 and (x+y)2=9, what is the value of y?

And the answer is not -1.. what is the trick here that I'm missing? The answer is supposed to be 5.
 
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Monique said:
If x+2y=2 and (x+y)2=9, what is the value of y?

And the answer is not -1.. what is the trick here that I'm missing? The answer is supposed to be 5.

[tex]x+2y=2[/tex]
so
[tex]x=2-2y[/tex]
so
[tex](x+y)^2=(2-2y+y)^2=(2-y)^2=9[/tex]
square root of both sides:
[tex]\pm (2-y)=3[/tex]
[tex]-3=2-y[/tex] or [tex]3=2-y[/tex]
So the solutions (note the plural) are:
[tex](-8,5)[/tex] and [tex](4,-1)[/tex]

I'm guessing you forgot that every number has two square roots. ;)
 
ahhh see? these little simple things.. thanks NateTG!

I should be doing other things at 2 in the morning
 
monique is a cutie :blush:
 

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